Prince of Wales' official 70th birthday photograph with his family was an "absolute nightmare" to plan because his sons blew "hot and cold" with their father, the book claims.
The photo released in 2018 featured the heir to the throne sitting on a bench with Prince George on his knee, and the Duchess of Cornwall and Princess Charlotte next to him.
Standing behind were Prince William and Kate, with the duchess holding Prince Louis, and Harry and Meghan.
A source said it was difficult to arrange as "neither William nor Harry made much of an effort to make themselves available", with the authors of the book describing Charles and Harry's relationship as "complicated".
But when Charles contracted Covid-19, Harry immediately telephoned his father to find out how he was, the book states. "The doctors described the Prince of Wales as in 'good spirits' and his symptoms as mild, it was still enough to fill Harry with worry," the authors wrote.
He immediately called Charles at Birkhall, his Scottish home where he was now quarantined. Harry regularly checked in on his father until he was out of quarantine and recovered "as well as Camilla, who isolated herself as a precaution".
Meanwhile, Meghan saw Prince Charles as a father figure and he was equally fond of her, the book claims. She is said to have formed such a close bond with Charles that she considers him her "second father".
He is said to have taken a "real shine" to her, describing her as a "sassy, confident beautiful American". A friend said: "He likes very strong, confident women. She's bright, and she's self-aware, and I can see why they've struck up a very quick friendship."
Meghan's first cup of tea with the Queen is also described in great detail in Finding Freedom, in a clear breach of royal protocol. Dismissing the notion that such occasions are meant to remain private, the book describes Meghan's first visit to "the inner sanctum of the Queen's private apartment".
"Harry kissed his grandmother on both cheeks as they walked into her sitting room," the authors wrote.
"Was she really meeting with the head of the Commonwealth? Today, however, it was just 'Granny' as Harry called the Queen, who sat down on the silk, upholstered, straight-back chair."